Piezoelectric laminate motion sensing apparatus and method

ABSTRACT

A motion sensing system utilizing piezoelectric laminates with predetermined surface electrode patterns disposed thereon utilizes a frequency selector to pass motion waves of predetermined frequencies and an electrical circuit for processing the electrical signals for transmission to an activating device for appropriate activation. In particular, the frequency selector is a low frequency bandpass filter for free-fall acceleration wave frequencies. By directing appropriate action, the present invention increases the applicability of the device upon which it is mounted (e.g., for military or other hostile environment use), decreases the possibility of damage, and lengthens its useful life.

CROSS-REFERENCE TO RELATED APPLICATION

This application is a continuation of, and claims the priority benefefitof U.S. application Ser. No. 09/908,047, filed Jul. 18, 2001, now U.S.Pat. No. 6,998,759.

FIELD OF THE INVENTION

This invention relates generally to motion sensing devices and moreparticularly to a conformable piezoelectric laminate sensing structureutilizing a distribute electrode pattern for sensing free-fall motionwaves.

BACKGROUND OF THE INVENTION

A point sensor/actuator (accelerometer or transducer) utilizing thepiezoelectric effect reacts to or induces force, displacement, oracceleration at a point in a structure embodying the sensor/actuator. Noa priori knowledge about the structure is needed to achieve the desiredsensing or actuating. Discrete point sensors/actuators to detect andcontrol the vibrations of flexible structures such as robot arms,satellite antennas and the like have been in existence for over thirtyyears. However, actuator/observer spillover due to residual(uncontrolled) vibration modes in conventional systems leads toinstabilities in closed-loop control systems. The independentmodal-space control method utilizing pre-filtering and modal filteringhas been proposed to solve the spillover problem. In one prior artinstance, a modal-filtering process generated signals from an array ofdiscrete point sensors simultaneously and then fed the signals into acontrol loop circuit, but the large number of signals and subsequentamount of signal processing required resulted in significant phasedelays in the control loop circuit, thereby rendering the systemunreliable at best and inoperable at worst.

Conventional point-sensors operate at specific given points on astructure to collect motion signals, or they may operate as differentstructures themselves or in operate in different states to detectdifferent specific motion/vibration signals. In cases where themeasurement of motions or vibrations itself is not influenced by thedevice to be measured, the motion sensing and measurement is relativelysimple. However, in practice, conventional point sensors are clearlyaffected by the characteristics of their own structure when making amotion detection and thus they are limited by an effective usablebandwidth (i.e., within which there is no self-effect).

Distributed surface electrode patterns and their directions ofpolarization can increase the effective use bandwidth of the sensors.Because electrodes can be distributed in space, in addition to beingable to detect the total motion of a body, the distributed force on thatbody (the force on particular parts of the body) can also be measured.However, because distributed sensing requires a sensor pattern specificto the structure in question, the sensing system must be re-designed foreach different application. Thus distributed sensing systems sufferedfrom lack of general applicability. This is the principal reason to datewhy distributed sensor systems have not been as widely used as pointsensor systems.

The piezoelectric effect is the phenomenon whereby certain materials,when subjected to a distorting force will produce an electricalpolarization and a subsequent electromotive force. Conversely, when anelectromotive force is applied to such a material, it will change itsshape in response to that emf. Thus, piezoelectric materials can be usedas motion sensors or actuators. However, conventional piezoelectricmaterials are typically crystalline or polycrystalline and thereforebrittle and not easily conformable.

SUMMARY OF THE INVENTION

It is an objective of the present invention to provide a miniaturedistributed sensing system that is applicable for many differentstructures, without the need for significant re-design. The inventioncomprises an effectively one-dimensional motion sensing system utilizingpiezoelectric laminates with predetermined surface electrode patternsdisposed thereon. A frequency selector passes motion waves ofpredetermined frequencies and an electrical circuit processes theelectrical signals and transmits them to an activating device foractivation in response to the electrical signals. In particular, thefrequency selector is a low frequency bandpass filter for free-fallacceleration wave frequencies. By directing appropriate action, thepresent invention increases the applicability of the device upon whichit is mounted (e.g., for military or other hostile environment use),decreases the possibility of damage, and lengthens its useful life.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic representation of a beam fixed to structure at oneend.

FIG. 2 is a schematic diagram showing the skew angle ±θ between thestructural principal axes and the material axes of a set of lamina.

FIG. 3 is a schematic representation of a PVF₂ lamina according to thepresent invention having a piezoelectric film and sandwichingelectrodes.

FIG. 4 is a schematic diagram of a section of a laminate in the xz-planedeformed due to a loading according to the present invention.

FIG. 5 is a schematic diagram of a piezoelectric lamina having disposedthereon a surface electrode in the upper and lower faces according tothe present invention.

FIG. 6 is a charge amplifier circuit schematic according to a preferredembodiment of the present invention.

FIG. 7 is a current amplifier circuit schematic according to a preferredembodiment of the present invention.

FIG. 8 is a schematic diagram of one embodiment of the present inventionshowing a piezoelectric lamina for sensing shearing stress motionsaccording to the present invention.

FIG. 9 is a schematic diagram of a suspended laminate beam in anembodiment of the present invention.

FIG. 10 is a schematic diagram of the sensor structure with the fixedend and free end represented as the axis crossing and maxima/minimapoints respectively according to the present invention.

FIG. 11 is a schematic diagram of the method of image utilized in thepresent invention for a wave propagation from the finite structure tothe infinite structure.

FIG. 12( a) is a gain versus frequency graph showing frequency responsecurves resulting from the output of a spatial wave filter implemented ina sensor structure according to the present invention.

FIG. 12( b) is a phase versus frequency graph showing the effect of thepresent invention on the system phase change.

FIG. 13( a) is a gain versus frequency graph showing the effect of theutilization of modal discrete point sensors according to the presentinvention.

FIG. 13( b) is a phase versus frequency graph showing a constant phaserelation for a significantly larger frequency range according to thepresent invention.

FIG. 14 is a schematic drawing of an exemplary disk drive having acasing and deposed thereon a motion detector according to the presentinvention.

FIG. 15 is a schematic drawing of a turning effect sensor according tothe present invention disposed on a disk drive casing.

FIG. 16 is a schematic drawing of a twist effect sensor according to thepresent invention disposed on a disk drive casing.

FIG. 17 is a schematic drawing of a compressing/stretching effect sensoraccording to the present invention disposed on a disk drive casing.

DETAILED DESCRIPTION OF THE INVENTION

The preferred embodiment of the present invention is a motionsensor/actuator utilizing conformable piezoelectric laminate sensorstructures having discrete and distributed surface electrode arrays. Inone preferred embodiment, extremely low frequency motions or vibrationsare sensed and the boundary conditions of the structure itself and otherspecial characteristics of the structure, such as its self-dampingfunction act to avoid phase delays in the control system and providecompensation for the entire system. The present invention utilizes anormal mode expansion distributed sensors design which, together withappropriate boundary conditions, produce a characteristic polynomialwave transmission spatial bandpass filter. The frequency responsefunctions of the distributed sensors provide an adjustment capabilityfor increasing the bandwidth of the measurement and/or increasing thefrequency selection, thereby providing a system suitable for detectionand actuation of different type motions.

In particular, the frequency selectivity and widen bandwidth make thepresent invention possessing the capability that can measure the startof a free-fall motion. The way and trace of forces exerting on presentinvention from a free-fall motion are different from all theconventional accelerometers and strain rate sensors. Conventionalaccelerometers and strain sensors measure external forces from thelocations they attached. Thus, only the mechanical forces propagate“through” the attaching site will be measured. Because of having topossessing enough bandwidth to measure any possible external forces,conventional sensors are made stiffer, and because of their sensorstructure they cannot have enough sensitivity for a particularbandwidth. Free-fall motion, on the contrary, does not transfer theirmechanical force from the attaching site. Its mechanism is based on thefact that the overall acceleration of the sensor and the attachedtesting structure is changed together due to free falling. Thisacceleration change does not like the acceleration that all theconventional sensors will encounter. It requires a sensor possesses ahighly frequency selectivity and sensitivity at that particularfrequency bandwidth to measure the free-fall motion. The presentinvention utilizing conformable piezoelectric laminate sensor structureshaving discrete and distributed surface electrode arrays to offer asensor that possess enough frequency bandwidth and sensitivity tomeasure the motion of a free falling. It should be pointed out that amotion sensor designed by the present invention is not a conventionalaccelerometer or a strain rate sensor. It is truly a free-fall sensor.

In a sensing operation, the charge generated by deformations in apiezoelectric material are collected by the array of surface electrodes,spatial filtering is performed, and for large, complex structures havingmany surface electrodes, parallel processing of signals avoids controlloop phase delays. In utilizing a wave mode formulation and a dispersionrelation in the design of the present invention, the distributed sensorshave transfer functions with amplitude response similar to low-passfiltering, thereby achieving non-causal compensation for control of thestructure.

The preferred embodiment of the present invention advantageouslyutilizes laminated sensing structures composed of polyvinylidenefluoride (PVF₂). However, it is understood by those in the art that anymaterial that exhibits the piezoelectric effect is within the scope ofthe present invention; for example, any material with ferroelectricbehavior such as poly(vinylidene fluroide-trifluorethylene) or VF₂VF₃,lead zirconate titanate or PZT, and the like.

Polyvinylidene fluoride polymer (PVDF or PVF₂) exhibits a strongpiezoelectric effect and is a flexible, conformable material havingrelatively low acoustic impedance and low Q value. It is rugged, lightweight, inexpensive and easily produced and cut, and is thereforesuitable for many applications such as the distributed sensors andactuators of the present invention.

The piezoelectric laminate of the present invention comprises thinlayers of material, some with piezoelectric properties and some withoutpiezoelectric properties. FIG. 1 is a schematic representation of a beam101 fixed to structure 102 at one end. Beam 101 undergoes three possiblemotions: bending in the y-axis and z-axis directions, twisting aroundthe x-axis, and stretching (extension or tension) in the x-axisdirection. Plates and beams are the fundamental elements of larger, morecomplicated structures, so the detection and control of the motions ofcomplex structures can be addressed in relation to the motions of a beamelement. The beam is extensible, compressible, twistable, andconformable and the composite of beam element motions constitutes themotion of the larger structure of which the beams are constituents.

Choosing each lamina to perform a specific function andactuating/sensing each lamina individually or in combination achievesdetection and control of the motions of the structure. Designing thesurface electrode pattern for each lamina determines the integratedspatial response. For sensing, the electric charge generated due to anexternal mechanical disturbance will be detected only if the charge iscollected by the surface electrode and transmitted to a detectingcircuit. Similarly, for actuating, only the parts of the lamina havingelectrodes will be affected by an externally applied field. Varying thepolarization profile within a lamina is achieved by repoling, and thestrength of the piezoelectric effect can be varied by doping, creatingtwo-phase piezoelectric composites, or through specific fabrication. Thepiezoelectric strength of a point in a lamina corresponds to a weightingfactor for the sensing/actuating. FIG. 2 is a schematic diagram showingthe skew angle ±θ between the structural principal axes x,1 and thematerial axes x′,1′ of each lamina. The skew angle is utilized toachieve torsional mode actuating/detecting in the present invention.FIG. 3 is a schematic representation of a PVF₂ lamina 300 according tothe present invention having a piezoelectric film 302 and electrodes 301and 303 sandwiching piezoelectric film 302. The rolling direction x,1and the poling direction z,3, are shown wherein dipoles 310 will begenerated by poling field 315. For example, rolling and poling isrequired for PVF₂ to be piezoelectric with the poling axis defined asthe z-axis and rolling (stretching) defined on the x-axis for uniaxiallystretched films. PVF₂ has symmetry (of a group mm2) where the x and yaxes are the normals of the two mirror planes and the z-axis hastwo-fold symmetry. The piezoelectric strain matrix is

$\begin{matrix}{d_{ip} = \begin{bmatrix}0 & 0 & 0 & 0 & d_{15} & 0 \\0 & 0 & 0 & d_{24} & 0 & 0 \\d_{31} & d_{32} & d_{33} & 0 & 0 & 0\end{bmatrix}} & (1)\end{matrix}$

The constitutive equations of a piezoelectric material is described(using the IEEE compact matrix notation) byT _(p) =c _(pq) ^(E) S _(q) −e _(kp) E _(k)  (2)D _(i) =e _(iq) S _(q)+ε_(ik) ^(S) E _(k)  (3)orS _(p) =s _(pq) ^(E) T _(q) +d _(ip) E _(k)  (4)D _(i) =d _(iq) T _(q)+ε_(ik) ^(T) E _(k)  (5)be generated by poling field 315. For example, rolling and poling isrequired for PVF₂ to be piezoelectric with the poling axis defined asthe z-axis and rolling (stretching) defined on the x-axis for uniaxiallystretched films. PVF₂ has symmetry (of a group mm2) where the x and yaxes are the normals of the two mirror planes and the z-axis hastwo-fold symmetry. The piezoelectric strain matrix is

$\begin{matrix}{d_{ip} = \begin{bmatrix}0 & 0 & 0 & 0 & d_{15} & 0 \\0 & 0 & 0 & d_{24} & 0 & 0 \\d_{31} & d_{32} & d_{33} & 0 & 0 & 0\end{bmatrix}} & (1)\end{matrix}$

The constitutive equations of a piezoelectric material is described(using the IEEE compact matrix notation) byT _(p) =c _(pq) ^(E) S _(q) −e _(kp) E _(k)  (2)D _(i) =e _(iq) S _(q)+ε_(ik) ^(S) E _(k)  (3)orS _(p) =s _(pq) ^(E) T _(q) +d _(ip) E _(k)  (4)D _(i) =d _(iq) T _(q)+ε_(ik) ^(T) E _(k)  (5)where the subscripts i, k=1′,2′,3′ and p, q =1′,2′,3′,4′,5′,6′. Thesubscripts represent the fields which remain constant, T_(p) and S_(p)represent stress and strain respectively, E_(k) is the electric fieldintensity, D_(i) is electric displacement, c_(pq) is the elasticstiffness matrix, s_(pg)=(c_(pg))^(−l) is the elastic compliance matrix,ε_(ij) is the permittivity matrix, e_(kp) is the piezoelectric stressmatrix and d_(iq) is the piezoelectric strain matrix.

From Eqns (1) and (4), applying an electric field along the z-axis willinduce only a normal strain along the material axes. Also, only thenormal strain can be detected by measuring electric displacement alongthe thickness direction (Eqns. (2)–(5)). Referring to FIG. 1, onlybending and stretching motions can be actuated or detected by apiezoelectric material with mm2 symmetry alone. Shear strain needs to begenerated in order to induce torsion in the beam. In the presentinvention, the skew angle θ (FIG. 2) is utilized to achieve torsionalmode actuating/detecting. This is done by introducing a d₃₆ matrixelement (Eqn. (1)) through the use of non-zero skew angles so thattorsional motion can be induced or detected. From Mohr's circle, it isknown that by rotating the plane of observation, the shear strain andnormal strain interchanges according to the tensor transformation law.Using the Kirchhoff hypothesis, there is a plane stress state, so thelaminae, when disposed in the laminate, is in a plane stress state.Expanding the Kirchhoff hypothesis into the piezoelectric laminatesyields the constitutive relationship of each lamina.

FIG. 4 is a schematic diagram of a section of a laminate in the xz-planedeformed due to a loading. Point C at the geometric mid-plane undergoessome displacement u₀ in the x-direction, the line normal to thegeometric mid-plane ABD remains straight and normal to the geometricmid-plane, the displacement of any point on the normal ABD, say of pointB, in the x-direction is given by a linear relationship,u_(B)=u₀−z_(B)α, where u₀ is the mid-plane displacement in thex-direction, z_(B) is the z-coordinate of point B measured from thegeometric mid-plane and α=∂w/∂x is the slope of the mid-plane withrespect to the z-axis, in other words the curvature. Thus the straindisplacement u in the x-direction for an arbitrary point at a distance zfrom mid-plane is

$\begin{matrix}{u = {u_{0} - {z\;\frac{\partial w}{\partial x}}}} & (6)\end{matrix}$and similarly for displacement in the y-direction

$\begin{matrix}{v = {v_{0} - {z\;\frac{\partial w}{\partial y}}}} & (7)\end{matrix}$from linear elasticity,

$\begin{matrix}\begin{matrix}{{S_{1} = \frac{\partial u}{\partial x}};} & {{S_{2} = \frac{\partial v}{\partial y}};} & {S_{6} = {\frac{\partial u}{\partial y} + \frac{\partial v}{\partial x}}}\end{matrix} & (8)\end{matrix}$therefore,

$\begin{matrix}\begin{matrix}{\begin{bmatrix}S_{1} \\S_{2} \\S_{6}\end{bmatrix} = {\begin{bmatrix}S_{1}^{0} \\S_{2}^{0} \\S_{6}^{0}\end{bmatrix} + {z\begin{bmatrix}k_{1} \\k_{2} \\k_{6}\end{bmatrix}}}} \\{\mspace{56mu}{= {\begin{bmatrix}{{\partial u_{0}}/{\partial x}} \\{{\partial v_{0}}/{\partial y}} \\{{{\partial u_{0}}/{\partial_{y}{+ {\partial v_{0}}}}}/{\partial x}}\end{bmatrix} + {{z\begin{bmatrix}{{- {\partial^{2}w}}/{\partial x^{2}}} \\{{- {\partial^{2}w}}/{\partial y^{2}}} \\{{- 2}\;{{\partial^{2}w}/{\partial x}}\;{\partial y}}\end{bmatrix}}.}}}}\end{matrix} & (9)\end{matrix}$The electrical displacement is given byD ₃ =e ₃₁(S ₁ ⁰ +zk ₁)+e ₃₂(S ₂ ⁰ +zk ₂)+e ₃₆(S ₆ ⁰ +zk ₆)+ε₃₃ ^(T) E₃  (10).

Gauss' Law gives the charge enclosed by a surface element S

$\begin{matrix}{{q(t)} = {\int_{S}^{\;}{D \cdot {\mathbb{d}\sigma}}}} & (11)\end{matrix}$where D is the electric displacement vector and do is the differentialarea normal vector of S. However, the utilization of this equation todescribe the charge enclosed in a portion of a piezoelectric lamina,results in a null value because the charge within a dielectric isneutral. Since charge is built up on the surface of a piezoelectriclamina when it is under an external force field, the present inventionutilizes an equivalent circuit to relate the closed-circuit chargesignal measured for the surface electrode to the force field. FIG. 5 isa schematic diagram of a piezoelectric lamina 500 having disposedthereon a surface electrode in the upper face 501 and a surfaceelectrode in the lower face 502. An equivalent circuit 510 has acapacitor 511 and resistor 512 in parallel. The surface charge built updue to mechanical action is analogous to the charge stored insidecapacitor 511 of equivalent circuit 510. The electric displacement isD=D₃e₃, where e₃ is a unit vector parallel to the z-axis as shown inFIG. 5. To measure the charge, the electric loop must be closed; thatis, the electrode must appear on both sides of lamina 500 (surfaceelectrodes 501 and 502) so that a charge moving in the (z,3)-directioncan be measured. More specifically, if surface electrode 501 is on theupper face (S¹) of lamina 500 and surface electrode 502 is on the lowerface (S²) of lamina 500, the portion of the electrode which is effectiveduring measurement is approximated by S⁽¹²⁾=S¹∩S² where S⁽¹²⁾ is theeffective surface electrode. Disposing such surface electrodes in apattern on lamina 500 defines the integration domain where all thepoints of interest are covered with surface electrodes on both sides oflamina 500. The closed circuit charge measured through the electrodes ofthe k^(th) layer is

$\begin{matrix}{{q_{k}(t)} = {\frac{1}{2}\left( {{\int{\int_{S^{(12)}{({z = z_{k}})}}^{\;}{D_{3}{\mathbb{d}x}\;{\mathbb{d}y}}}} + {\int{\int_{S^{(12)}{({z = z_{k - 1}})}}^{\;}{D_{3}\;{\mathbb{d}x}\;{\mathbb{d}y}}}} +} \right)}} & (12)\end{matrix}$Substituting Eqns (9) and (10) into Eqn (12) and using the fact thate₃₁, e₃₂, e₃₆, S₁ ⁰, S₂ ⁰, k₁, k₂, k₆, are all independent of z withineach lamina, the general sensor charge equation according to the presentinvention is

$\begin{matrix}{{q_{k}(t)} = {{\int{\int_{S^{(12)}}^{\;}{\left\lbrack {{{e_{31}\;\frac{\partial u_{0}}{\partial x}} + {e_{32}\;\frac{\partial v_{0}}{\partial y}} + {e_{36}\left( {\frac{\partial u_{0}}{\partial y} + \frac{\partial v_{0}}{\partial x}} \right)} +} \in_{33}^{T}\; E_{3}} \right\rbrack\;{\mathbb{d}x}\;{\mathbb{d}y}}}} - {z_{k}^{0}{\int{\int_{S^{(12)}}^{\;}{\left\lbrack {{e_{31}\;\frac{\partial^{2}w}{\partial x^{2}}} + {e_{32}\;\frac{\partial^{2}w}{\partial y^{2}}} + {2\; e_{36}\;\frac{\partial^{2}w}{{\partial x}\;{\partial y}}}} \right\rbrack\;{\mathbb{d}x}\;{\mathbb{d}y}}}}}}} & (13)\end{matrix}$where z_(k) ⁰=(z_(k)+z_(k−1))/2 and u and v are the displacements in thex and y directions respectively. The first part of Eqn (13) representsthe response of piezoelectric lamina 500 to the in-plane strain, and win the second part of Eqn (13) represents the flexural (bending)displacement, which is piezoelectric lamina 500 acting as a sensor'sresponse to an out-of-plane strain. To relate the charge signal to themechanical deformation of the structure (system dynamics), the electricfield E₃ is set to zero by short-circuiting the surface electrodes onboth sides of piezoelectric lamina 500. Thus, Eqn (13) is theclosed-circuit charge sensor equation relating the in-planedisplacements and the curvature of the plate to the output signal. Sincei(t)=dq/dt, a general current sensor equation according to the presentinvention is

$\begin{matrix}{{i_{k}(t)} = {{\int{\int_{S^{(12)}}^{\;}{\left\lbrack {{e_{31}\;\frac{\partial u_{0}}{\partial x}} + {e_{32}\;\frac{\partial v_{0}}{\partial y}} + {e_{36}\left( {\frac{\partial u_{0}}{\partial y} + \frac{\partial v_{0}}{\partial x}} \right)}} \right\rbrack\;{\mathbb{d}x}\;{\mathbb{d}y}}}} - {z_{k}^{0}\;{\int{\int_{S^{(12)}}^{\;}{\left\lbrack {{e_{31}\;\frac{\partial^{3}w}{{\partial x^{2}}\;{\partial t}}} + {e_{32}\;\frac{\partial^{3}w}{{\partial y^{2}}{\partial t}}} + {2\; e_{36}\;\frac{\partial^{3}w}{{\partial x}\;{\partial y}\;{\partial t}}}} \right\rbrack\;{\mathbb{d}x}\;{\mathbb{d}y}}}}}}} & (14)\end{matrix}$

In operation, to detect strain or displacement, a charge amplifier isutilized. FIG. 6 is a circuit schematic according to a preferredembodiment of the present invention. The circuit comprises a sensor 610,designed utilizing Eqn (13), coupled to the negative input of a chargeamplifier 620, which is coupled in series with a capacitor 630 and avariable resistor 631. The positive input of charge amplifier 620 isgrounded. Charge amplifier 620 amplifies the acceleration oracceleration rate signal generated by sensor 610. The output of chargeamplifier 620 a(t) is the signal to the device to be sensed for motionto initiate a responsive action; for example, a servo-mechanism causinga disk drive read/write head to leave the disk. To detect strain rate orvelocity, the present invention utilizes a current amplifier, forexample constructed from a regular operational amplifier. FIG. 7 shows acircuit schematic according to an embodiment of the present invention.The circuit comprises a sensor 710, designed according to Eqn (13),coupled to the negative input of a current amplifier 720 which is inparallel with a variable resistor 731. Current amplifier 720 amplifiesthe acceleration or acceleration rate signal generated by sensor 710.The output of current amplifier 720 a′(t) is the signal to the devicethat is motion-sensed to initiate an action: for example aservo-mechanism causing a disk drive read/write head to leave the disk.

For PVF₂, the piezoelectric stress matrix has no e₃₆ element (Eqn (1)).In order to have a value, the skew angle θ of the material's principalaxis and structural axis must be non-zero to produce a measurableshearing stress. In an embodiment of the present invention, thepiezoelectric stress matrix elements e31 and e32 are equal when θ is 45°and −45° respectively. FIG. 8 is a schematic diagram of one embodimentof the present invention showing a piezoelectric lamina 800 for sensingshearing stress motions. The dotted lines, for example 801 and 802, inpiezoelectric lamina 800 indicate the direction of the principal axis oflamina 800. Utilizing surface electrodes polarization directions shownas the 45° angle from the normal to the principal axis direction asshown in panels 820 and 830, the calculation of the surface integralfrom Eqn (13) achieves the desired piezoelectric sensor effect, andprovides an automatic canceling axial stress effect to eliminate thestress in the principal axis direction 801, which stress affects themotion sensing signal.

For beam or columnar structures undergoing only pure compression or puretension, the relationship between the sensor deformation and the stressis

$\begin{matrix}{ɛ_{x} = \frac{\partial u}{\partial x}} & (15)\end{matrix}$which is applicable for all types of cross sections. For pure torsion,the relationship for the stress and the torsion is

$\begin{matrix}{\gamma_{xy} = {\frac{\partial u}{\partial y} + \frac{\partial v}{\partial x}}} & (16)\end{matrix}$For pure bending, the relationship between stress and bendingdisplacement is

$\begin{matrix}{ɛ_{x} = {- \frac{\partial^{2}w}{\partial x^{2}}}} & (17)\end{matrix}$Since the x-axis in Eqns (15) and (16) is the beam's axial coordinate,and the x-axis of Eqn (17) is the principal axis of the lamina or beam,the shear stress relation in Eqn (17) can be substituted into thecolumnar coordinate system and Eqn (15) can be written as

$\begin{matrix}{\gamma_{xy} = {{\frac{\partial u}{\partial y} + \frac{\partial v}{\partial x}} = {{r\;\frac{\mathbb{d}\theta}{\mathbb{d}x}} = ɛ_{\theta\; z}}}} & (18)\end{matrix}$where r is the radius of the columnar beam and Eqn (13) is now (forcolumns only)

$\begin{matrix}{{q(t)} = {\int{\int_{S^{(12)}}^{\;}{{{FP}_{0}\left\lbrack {{e_{31}\frac{\partial u}{\partial x}} + {e_{32}\frac{\partial v}{\partial y}} + {e_{36}\left( {\frac{\partial u}{\partial y} + \frac{\partial v}{\partial x}} \right)}} \right\rbrack}\mspace{11mu}{\mathbb{d}x}\;{\mathbb{d}y}}}}} & (19)\end{matrix}$where F is the distributed effective surface electrode function and P₀is the strength of polarization. For PVF₂, e₃₆ provides shear stresseffect only when the piezoelectric lamina principal axis and theprincipal axis of the structure are at an angle to each other. Thus thepresent invention utilizes the relative orientation of the piezoelectricmaterial and the structure to directly detect different types of stressand avoid spurious signals. In other words, when the principal axis of apiezoelectric laminate disposed on a columnar beam is collinear with theprincipal axis of the column, then the torsional stress will not affectthe output signal which will only be responsive to the axialdeformation.

On the other hand, when a two-dimensional piezoelectric laminate sensorstructure only undergoes out-of-plane stress, Eqn (13) can be simplifiedas

$\begin{matrix}{{q_{k}(t)} = {{- z_{k}^{0}}{\int{\int_{S^{(12)}}^{\;}{{F\left( {x,y} \right)}\;{{P_{0}\left( {x,y} \right)}\left\lbrack {{e_{31}^{0}\frac{\partial^{2}w}{\partial x^{2}}} + {e_{32}^{0}\frac{\partial^{2}w}{\partial y^{2}}} + {2\; e_{36}^{0}\frac{\partial^{2}w}{{\partial x}\;{\partial y}}}} \right\rbrack}\;{\mathbb{d}x}\;{\mathbb{d}y}}}}}} & (20)\end{matrix}$where Z_(k) ⁰ is the thickness of the k^(th) lamina.

In the case where the motion of the sensor is only about the x-axis, Eqn(13) can be simplified as

$\begin{matrix}{{q_{r}(t)} = {e_{31}\;{\int_{0}^{a}{{\zeta(x)}\;\frac{\partial u}{\partial x}{\mathbb{d}x}}}}} & (21) \\{{q_{s}(t)} = {e_{36}{\int{\int_{S^{(12)}}^{\;}{{{\zeta\left( {x,y} \right)}\left\lbrack {\frac{\partial u}{\partial x} + \frac{\partial v}{\partial y}} \right\rbrack}\;{\mathbb{d}x}\;{\mathbb{d}y}}}}}} & (22) \\{\mspace{45mu}{= {e_{36}r^{2}\;{\int_{S^{(12)}}^{\;}{{\zeta(x)}\;\frac{\mathbb{d}\theta}{\mathbb{d}x}{\mathbb{d}x}}}}}} & \; \\{{q_{p}(t)} = {{- z^{0}}e_{31}^{0}\;{\int_{0}^{a}{{\zeta(x)}\;\frac{\partial^{2}w}{\partial x^{2}}{\mathbb{d}x}}}}} & (23) \\{{\zeta(x)} = {\int_{{- b}/2}^{b/2}{{F\left( {x,y} \right)}\;{P_{n}\left( {x,y} \right)}\;{\mathbb{d}y}}}} & (24)\end{matrix}$

Eqn (24) is the effective surface electrode distribution and the qsubscripts r, s, and p in Eqns (21) to (23) indicate that those are thesensor equations for rods, axial direction, and laminates respectively.F(x,y) is the effective surface electrode distribution function andP_(n)(x,y) is the polarization strength in the n-direction. With respectto the rod and laminate, when n equals 1 (i.e., P₁(x,y)), that is thepolarization strength represented by the piezoelectric strain matrixelement e₃₁; and when n equals 6, (i.e., P₆(x,y)), then the polarizationstrength is represented by the piezoelectric strain matrix element e₃₆.The a is the sensor's length on the x- axis and b is the width area onthey-axis. Eqn (21) assumes a one-dimensional rod undergoing purecompression or pure tension stress only in the x-axis direction. Eqn(22) assumes a one-dimensional shaft undergoing pure torsion stress onlyin respect to the x-axis, and Eqn (23) assumes a one-dimensionalprojected beam undergoing pure bending stress only in respect to thex-axis. Thus, all types of structural motion will only be with respectto the x direction and t (time). Also, u represents the displacement ofa rod undergoing compression or tension in-plane stress, θ is theangular displacement of the rod undergoing twisting stress, and w is theone-dimensional flexural deflection of the laminate or beam. Regardlessof what kind of motion of the effective surface electrode ζ(x), it isonly effected on the x-axis of the structure, so the same configurationof the effective surface electrode on any one-dimensional structure willhave the same effect. Therefore, any structure in accord with the aboveassumptions can be handled by the sensor structure of the presentinvention.

The governing equations for a R damping one-dimensional rod, axis, andlaminate according to the present invention are

$\begin{matrix}{{{E\;\frac{\partial^{2}{u\left( {x,t} \right)}}{\partial x^{2}}} + {R\;\frac{\partial^{3}{u\left( {x,t} \right)}}{{\partial t}\;{\partial x^{2}}}} - {\rho\;\frac{\partial^{2}{u\left( {x,t} \right)}}{\partial t^{2}}}} = 0} & (25) \\{{{G\;\frac{\partial^{2}{\theta\left( {x,t} \right)}}{\partial x^{2}}} + {R\;\frac{\partial^{3}{\theta\left( {x,t} \right)}}{{\partial t}\;{\partial x^{2}}}} - {\rho\;\frac{\partial^{2}{\theta\left( {x,t} \right)}}{\partial t^{2}}}} = 0} & (26) \\{{{{EI}\;\frac{\partial^{4}{w\left( {x,t} \right)}}{\partial x^{4}}} - {R\;\frac{\partial^{3}{w\left( {x,t} \right)}}{{\partial t}\;{\partial x^{2}}}} + {\rho\; A\;\frac{\partial^{2}{w\left( {x,t} \right)}}{\partial t^{2}}}} = 0} & (27)\end{matrix}$where E in Eqn (25) is the pressure coefficient, ρ is the density, u isthe structure's cross-sectional displacement, x is the structure'scross-sectional displacement relative to the rod axis direction. G inEqn (26) is the twisting moment strength coefficient, θ is the angle oftwist, x is the structural cross-section's twisting angle relative tothe axial direction of the rod. EI in Eqn (27) is the flexural rigiditycoefficient, A is the structure cross-section, and x is the bendingdisplacement relative to the principal axis.

If a one-dimensional simple harmonic vibration sensor structure isdisposed in the structure to be measured, then the structure's physicalvibration is represented byV(x,t)=V(x)e ^(jax)so for Eqns (25) to (27), the wavenumber k and the frequency ωrelationship are given by the dispersion relations between k-space andω-space

$\begin{matrix}{k^{2} = {{- \frac{\rho}{E + {j\;\omega\; R}}}\omega^{2}}} & (28) \\{k^{2} = {{- \frac{\rho}{G + {j\;\omega\; R}}}\omega^{2}}} & (9) \\{k^{2} = {{j\;\frac{R}{2\;{EI}}} \pm {\frac{\left( {{4{EI}\;\rho\; A} - R^{2}} \right)^{1/2}}{2{EI}}\omega}}} & (30)\end{matrix}$so utilizing the characteristic wave propagation polynomial for thesensor structures displacement to enter the propagation state is givenrespectively by

$\begin{matrix}{{u\left( {x,t} \right)} = {\left\lbrack {{w_{lp}{\mathbb{e}}^{j\; k_{lp}x}} + {w_{rp}\;{\mathbb{e}}^{{- j}\; k_{rp}x}}} \right\rbrack\;{\mathbb{e}}^{j\; w\; t}}} & (31) \\{{\theta\left( {x,t} \right)} = {\left\lbrack {{w_{lp}\;{\mathbb{e}}^{j\; k_{lp}x}} + {w_{rp}\;{\mathbb{e}}^{{- j}\; k_{rp}x}}} \right\rbrack\;{\mathbb{e}}^{j\; w\; t}}} & (32) \\{{w\left( {x,t} \right)} = \left\lbrack {{w_{lp}\;{\mathbb{e}}^{{({{j\; k_{R}} - k_{I}})}\; x}} + {w_{rp}\;{\mathbb{e}}^{{- j}\;{({{j\; k_{R}} - k_{I}})}\; x}} +} \right.} & (33) \\{\left. \mspace{104mu}{{w_{le}\;{\mathbb{e}}^{{({k_{R} - {j\; k_{I}}})}\; x}} + {w_{re}\;{\mathbb{e}}^{{- {({k_{R} - {j\; k_{I}}})}}\; x}}} \right\rbrack\;{\mathbb{e}}^{j\; w\; t}} & \;\end{matrix}$where recall that u is the strain displacement, θ is the angulardisplacement, and w is the flexural displacement. w_(lp), w_(rp) are theamplitudes of the left and right propagating waves respectively, andw_(le) and W_(re) are the amplitudes of the left and right evanescentwaves respectively. From Eqns (31) and (32), it can be seen that the rodand axis wave transfer are all only propagating waves having identicalwave characteristics with only the state of vibration and strengthcoefficient being different, and jk_(lp) and −jk_(rp) are the imaginaryroots of the dispersion relation. In contrast to the beam structure, thelaminate wave transfer characteristic is a combination of the effect ofthe propagating and the evanescent waves, and k_(r) and k_(l) are thefour root solutions to the dispersion relation. The four numbers willvary according to the boundary conditions and these four waves (rightand left propagating and evanescent) are utilized for the design of thepresent invention.

If Eqns (31) to (33) are substituted into Eqns (21) to (23)respectively, and if damping is ignored, the piezoelectric equations are

$\begin{matrix}{{q_{r}(k)} = {{jke}_{31}{\int_{0}^{a}{{{\zeta(x)}\left\lbrack {{w_{lp}e^{jkx}} - {w_{rp}e^{- {jkx}}}} \right\rbrack}{\mathbb{d}x}}}}} & (34) \\{{q_{s}(k)} = {{jke}_{36}r^{2}{\int_{0}^{a}{{{\zeta(x)}\left\lbrack {{w_{lp}e^{jkx}} - {w_{rp}e^{- {jkx}}}} \right\rbrack}{\mathbb{d}x}}}}} & (35) \\{{q_{p}(k)} = {{- z_{k}^{0}}e_{31}k^{2}{\int_{0}^{a}{{{\zeta(x)}\left\lbrack {{{- w_{lp}}e^{jkx}} - {w_{rp}e^{- {jkx}}} + {w_{le}e^{kx}} + {w_{re}e^{- {kx}}}} \right\rbrack}{\mathbb{d}x}}}}} & (36)\end{matrix}$where r is the radius of the shaft. From Eqns (34) to (36), it can beseen that a spatial wave filter utilizes the two wave modes to transformthe effective surface electrode ζ(x). From Eqns (34) and (35),regardless of compression, stretching, or twisting motions, the sensorequations are all left or right propagating characteristic waves and theeffects are the same except that the output values are different. Thusany sensor structure's sensing equation that can be expressed as asecond-order general equation such as

$\begin{matrix}{{q(k)} = {{jk}\;\Lambda{\int_{0}^{a}{{{\zeta(x)}\left\lbrack {{w_{lp}e^{jkx}} - {w_{rp}e^{- {jkx}}}} \right\rbrack}{\mathbb{d}x}}}}} & (37)\end{matrix}$where Λ is the integrated piezoelectric stress constant for differentstress waves. From Eqn (34), the Λ for a rod is e₃₁, and from Eqn (35)the Λ for a shaft is e₃₆r². Eqn (36) is the linear superposition of thepropagating and evanescent waves for bending effect sensor structures.The effective surface electrode ζ(x) is a function solely of x, andtherefore only the axial or principal axis, so a one-dimensional sensorstructure, regardless of whether it undergoes pure compression, puretension, pure torsion, or pure bending motions, can be applied todifferent motions to provide the same wave filter frequency selectioneffect.

The propagating waves discussed above are for infinite surfaces, but asEqns (36) and (37) describe, the structures are of course finite. Thepresent invention achieves practical application through the utilizationof a windowing function. In one embodiment, the windowing conceptintroduced by F. J. Harris (Proceedings of the IEEE, Vol. 66, No. 1,January 1978, pp 51–83) is advantageously utilized. The presentinvention introduces a window function h(x) factor on the surfaceelectrode equations which is non-zero over the structure in question andidentically zero outside of the structure. Then utilizing Laplacetransforms, the selection of an appropriate window function, f(x)becomesf(x)=h(x)ζ(x)w _(ml)  (38)where w_(ml) is a constant. Generally, each respective relativewavenumber k in Eqns (36) and (37) is

$\begin{matrix}{{L\left\lbrack {{f(x)};s} \right\rbrack} = {\int_{- \infty}^{\infty}{{f(x)}e^{- {sx}}{\mathbb{d}x}}}} & (39)\end{matrix}$where for beam structures, s=jk and −jk; for bending effect sensorstructures, s=jk, −jk, k, −k; and f(x) is the windowed effective surfaceelectrode function utilizable for infinite extent structures.

A significant objective achieved by the present invention is that thegain and phase function can be separated so that the piezoelectriccomponent's effective surface electrode function f(x) is altered so asto adjust the gain of the frequency response function of the sensorapparatus while not influencing the phase characteristic. Thiseffectively increases the useful bandwidth and stability and furthermorein the system feedback loop, directly provides compensation capability,thereby enhancing total system performance.

In accordance with a preferred embodiment of the present invention, afree fall sensor disposed on a disk drive provides a low pass wavefilter effect which can eliminate high frequency noise thereby obviatingconventional electronic wave filter gain adjustment-induced phase lag.This is achieved by utilizing waves as a basis to measure theacceleration and rate of acceleration of a falling body.

From Eqns (36) and (37), regardless of what the sensor structure is,utilizing similar independently designed gain and phase functions in themotion sensing apparatus according to the present invention, providesidentical spatial frequency selection. In a preferred embodiment of thepresent invention, a miniature one-dimensional suspended laminatedesigned with a low-pass filter characteristic frequency selector isdisposed on the casing of a disk drive for detecting a free fall signal.By signaling appropriate damage-avoidance action, the present inventionincreases the applicability of the disk drive (e.g., for military orother hostile environment use), decreases the possibility of damage, andlengthens its useful life.

Because the gain and phase function can be independently designed in thesensors of the present invention, utilizing Laplace transforms, thespatial filter effect is achieved only for the zero origin of theLaplace transform pair. From Eqn (36), the independently designed gainand phase function of the motion sensor allows specific designing for awave region. The dispersion relation Eqn (30) is the transformation tothe frequency domain, thereby achieving control of the sensor structuresystem frequency response function. From Eqn (33), the present inventionassumes that the different designs are in simple harmonic resonance;that is, the term exp(−iωt) is intentionally ignored. If the sensingpoint is not at the source of the motion of the sensor structure, thenthere will be a discrepancy with the simple harmonic motion assumption.Because the motion source is entered at a stationary point of thesuspended laminate, the fixed point of the sensor structure is chosen asthe origin point of the design, thereby avoiding any discrepanciescaused by the position of the motion source and the design point centerbeing different. Under this design, the present invention's frequencyresponse will only reflect the characteristic response of the sensorstructure.

FIG. 9 is a schematic diagram of an embodiment of the present inventionshowing a suspended laminate beam 900 having an origin point 901 throughwhich motions pass from the structure 902 to beam 900. Beam 900 has afixed end 920 joined to a base head 910 which is in turn attached to abase 941 . Beam 900 also has a free end 930. A schematic rendition of acircuit interface 940 is coupled to beam 900 for transmittingacceleration and acceleration rate signals to, for example, a disk drivesystem (not shown). According to the present invention the wave transfervia the piezoelectric sensor elements on beam 900 produces the spatialwave filters so that when the waves in beam 900 propagate back andforth, they continually “see” the piezoelectric laminate and surfaceelectrodes composing the piezoelectric sensing elements. A weightingfunction is then utilized to reflect the effect on the wave transfer ofthe different widths of the sensor materials along the y-axis enteringthe sensor structures, thereby producing the spatial wave filter of thepresent invention.

When the waves reach the boundary of the sensing structure, there willbe a phase change or energy dissipation due to different boundaryconditions, and the free end and the fixed end of beam 900 are the mostlikely boundary condition determiners. The present invention utilizesthe concept of “method of image” (cf. K. G. Graff, Wave Motion inElastic Solids) to address the limited space wave correspondencerelation with an unlimited space wave. Utilizing this approach, the wavetransmission at the free end of beam 900 will experience no phasechange, therefore except for when the direction of propagation isdirectly opposite, the wave will be continuous. However, wavetransmission at the fixed end of beam 900 will experience a 180° phasechange. Therefore, the present invention's independent gain and phasefunction designs successfully solves the phase delay problem.

FIG. 10 is a schematic diagram of the method of image utilized in thepresent invention for a wave propagation from the finite structure tothe infinite structure. The dotted lines triangle points are the fixedend 920 (FIG. 9) and free end 930 (FIG. 9) Thick solid line 1010represents a wave propagating through the structure. Dotted line 1012represents a finite piezoelectric sensor structure wave transformed intoan infinite wave utilizing the method of image expansion. Curved line1030 represents the gain and phase function of a bidirectional wavepropagating in the structure according to the independently designedgain and phase function of the present invention where the expansion ininfinite space being an odd function can be clearly seen. From thedesign viewpoint, the leftward and rightward propagating waves on thetwo sides of the same shaped evanescent and propagating wave generatethe same signal. Similarly, the two waves each leaving the center alsogenerate the same signal. The independently designed gain and phasefunction applied to the sensing structure's frequency response functiongenerates gain yet does not change the phase is because (from the designviewpoint) its past, present and future information are all present.Therefore, gain is achieved but phase is not changed by the presentinvention. If effective surface electrodes situated at the sides of thestructure's center point are symmetric, then eqn (36) is

$\begin{matrix}{{q(k)} = {{- z_{k}^{0}}e_{31}{k^{2}\left\lbrack {{\left( {{- w_{lp}} + w_{rp}} \right){\int_{- a}^{a}{{f(x)}e^{- {jkx}}{\mathbb{d}x}}}} + {\left( {w_{le} + w_{re}} \right){\int_{- a}^{a}{{f(x)}e^{- {kx}}{\mathbb{d}x}}}}} \right\rbrack}}} & (40)\end{matrix}$Thus, the present invention is a system providing a low pass filter thatgenerates no phase change through the proper selection of a surfaceelectrode function f(x). In other words, the spatial frequency selectoraccording to the present invention increases gain yet does not changethe phase and frequency relationship.

From Eqn (40), the propagation wave and the evanescent wave are in theform of natural logarithms so when the surface electrode has a naturallog for its basis function, it can effectively control the spatialfrequency selection characteristic curve. In other words, knowing thesurface electrode's basis function gives the spatial filter'scharacteristic. Similarly, generating the desired piezoelectric sensorconditions from the methods of the present invention allows optimumdesign and manufacture of an appropriate sensor for a specific use.

Setting the effective surface electrode as e^(−α|x|), from the Laplacetransform pair, the odd function spatial frequency selection functiondirectly enters a low-pass filter into the sensing structure's transferfunction, the transfer function being s/(α²−s²), where α is the selectedcorner frequency of the low-pass filter and s is −jk or −k. However,because its value at the boundary is not zero, it is not possible toextend to an infinite space. Therefore, again utilizing the windowfunction, setting the boundary wave's weighting function to zero, thetransfer function can be extended to the boundaryless region. Utilizingthe method of image technique, and taking into consideration thesuspended beam's boundary characteristics, a sine function directlyextends to the boundaryless area. FIG. 11 is a schematic diagram of thesensor structure 1110 with the fixed end 1120 and free end 1130represented as the axis crossing and maxima/minima points respectively.From the Laplace pairs, 0 to ∞ transfer function is α/(α²+S²), and 0 toto −∞ transfer function is −α/(α²+S²), thus the sine function cannotprovide any frequency selection for the effective surface electrode. Thepresent invention utilizes this characteristic to effect an effectivesurface electrode function asf(x)=e ^(−α|x|) −c sin [β(x)]  (41)where β makes the sine function a ¼ factor of the period in the finitespace, c makes the surface electrode function boundary value zeroweight. Substituting Eqn (41) into (40), the two surface electrodecombined sine function will not generate any effect on the spatialfilter's filter effect. Eqn (40) for a low frequency characteristicselection of the present invention sensor equation is represented by

$\begin{matrix}{{q(k)} = {{- z_{k}^{0}}e_{31}{k^{2}\left\lbrack {{\left( {{- w_{lp}} + w_{rp}} \right)\frac{s}{\alpha^{2} - s^{2}}} + {\left( {w_{le} + w_{re}} \right)\frac{s}{\alpha^{2} - s}}} \right\rbrack}}} & (42)\end{matrix}$where s is the propagating wave and the evanescent wave's transformsparameter −jk and −k respectively. From Eqn (42), the presentinvention's low-pass filter generates no phase delay (cf. FIG. 12( b)).Furthermore, the sensing structure itself will have a decreasedself-resonance effect and increased useful frequency range andstability. Since the propagating and evanescent waves transformparameters are different, the sensors transfer function are zero, andEqn (42) becomes

$\begin{matrix}{{q(k)} = {{- z_{k}^{0}}e_{31}{{k^{2}\left\lbrack {{\left( {{- w_{lp}} + w_{rp}} \right)\frac{j}{\alpha^{2} - s^{2}}} + {\left( {w_{le} + w_{re}} \right)\frac{1}{\alpha^{2} - s^{2}}}} \right\rbrack}.}}} & (43)\end{matrix}$Before the frequency value reaches the corner frequency value (α=−40dB/decade) extreme, there will be a 20 dB/decade zero point having nophase delay. Thus the present invention becomes a −20 dB/decade low passfrequency selector.

The present invention's independent gain and phase function designproviding a low pass frequency selector effect has the same capabilityas a second-order system. From Eqn (37) for a beam structure, only thepropagating wave effect need be considered, and for a beam structure asthe sensing structure, measuring the physical motion produced bycompression or twisting of a free fall body can be represented in asensor equation according to the present invention as

$\begin{matrix}{{q(k)} = {{jk}\;{\Lambda\left( {w_{lp} - w_{rp}} \right)}\frac{jk}{\alpha^{2} + k^{2}}}} & (44)\end{matrix}$

FIG. 12( a) is a gain versus frequency graph showing frequency responsecurves resulting from the output of a spatial wave filter implemented ina sensor structure according to the present invention. It can be seenthat frequency response curve 1220 advantageously utilizing a spatialwave filter according to the present invention can utilize frequencyband 1250 whereas a sensing system not utilizing a spatial wave filtercan only utilize frequency band 1240 which is considerably narrower.FIG. 12( b) is a phase versus frequency graph showing the effect of thepresent invention on the system phase change. Frequency response curves1260 and 1270 assume the gain frequency response curve (idealized) ofFIG. 12( a). Curve 1260 is frequency response curve utilizing thepresent invention, showing no phase change over the frequency domain,whereas curve 1270 is the phase change resulting from conventionalsystems. FIG. 13( a) is a gain versus frequency graph showing the effectof the utilization of modal discrete point sensors according to thepresent invention. It is clear from FIG. 13( a) that frequency responsecurve 1320, which is a result of the implementation of a modal discretepoint sensor system can utilize the bandwidth 1340 which is considerablywider than the conventional sensing systems 1310 which covers onlybandwidth 1330. FIG. 13( b) is a phase versus frequency graph showingthe phase shift for curve 1311 where it can be seen that curve 1321provides constant phase relation for a significantly larger frequencyrange. It should be noted that in utilizing the spatial wave filter andmodal approach, the system gain response function is adjustable, andfurther it will not follow the conventional causal method of adjustingphase in prior art electronic wave filters. The present inventionachieves adjustment of the frequency response characteristic of systemgain while not causing a phase shift in the sensing system. Gain andphase function are each utilized to design the motion detectionapparatus of the present invention.

Thus it is clear that the present invention not only increases theeffective spatial wave bandwidth of the sensing/actuation, but alsoresults in no system phase change. In the feedback circuit, the presentinvention provides frequency selection and compensating in the frequencyresponse effect. Thus the present invention is applicable to manydifferent kinds of structures.

For free fall sensing, the present invention can give an instantaneoussignal before impact with the ground to warn the system being monitored,enabling damage prevention measures (for example, in disk drives,ordering the read/write head of a disk drive to move away from thedisc). Although the descriptions given below will be primarily directedto notebook computer hard disk drives, it is understood by those in theart that any apparatus wherein motion detection is required is asuitable application of the present invention.

FIG. 14 is a schematic drawing of an exemplary disk drive 1400 having acasing 1420 and deposed thereon a motion detector 1410 according to thepresent invention to detect motions caused by impacts and unpredictedmotions which may cause improper read/write operations. The presentinvention, upon detection of certain motions, will cause read head 1430to temporarily leave disk 1440 to avoid damage or data corruption.

FIG. 15 is a schematic drawing of a turning effect sensor 1510 fordetecting turning motions according to the present invention by diskdrive casing 1520 upon which it is disposed. FIG. 16 is a schematicdrawing of a twist effect sensor 1610 for detecting twisting motions ofdisk drive casing 1620 according to the present invention. FIG. 17 is aschematic drawing of a compressing/stretching effect sensor 1710,according to the present invention, for detecting compression or tensionof the disk drive. Sensor 1710 is disposed upon disk drive casing 1720.

An embodiment of the present invention described above is utilized incomputer hard disk drives. In another embodiment, the present inventionis utilized in precision instruments and machinery, including robots.Various embodiments are utilized in systems requiring high precisionsensing of different types of motion. Embodiments of the presentinvention have been utilized in feedback control systems, fail-safe (oruninterruptable continuous) systems, and manufacturing operations.

A high percentage of notebook computer malfunction is due to impact ofthe computer with hard surfaces, including falling contact with theground. Impacts take only microseconds while the scan operation of theread/write head on hard disks takes at least several miniseconds. Thusit is practically impossible to direct the read/write head to leave thedisk in time to prevent corruption of data and/or (in the worst case)damage to the read/write head solely by detecting the impact. But thepresent invention detects the gravitational acceleration of the fallingmotion of the computer as a whole. Thus there is no need to wait for theimpact force to sense that something bad has happened. Conventionalaccelerometers are not capable of detecting such forcing mechanism. Thepresent invention advantageously utilizes the fact that a body willundergo an instant of external force at the instant of entering the freefall state. It is precisely this extremely short force that is detectedby the present invention. The state of free fall for a dropped notebookcomputer typically lasts for approximately 0.45 seconds (or subseconds).This time is generally long enough to enable the action of moving theread/write head. In the case where the falling height is so small thatthere is insufficient time to move the read/write head, it may bepresumed that the impact will be correspondingly small so that little orno damage or corruption of data occurs. An impact can be described by aTaylor expansion as

${f\left( {t->0^{+}} \right)} = {{f(0)} + {\frac{\mathbb{d}{f\left( {t = 0^{+}} \right)}}{\mathbb{d}t}t} + {\frac{\mathbb{d}^{2}{f\left( {t = 0^{+}} \right)}}{\mathbb{d}t^{2}}\frac{t^{2}}{2!}} + {\frac{\mathbb{d}^{3}{f\left( {t = 0^{+}} \right)}}{\mathbb{d}t^{3}}\frac{t^{3}}{3!}} + \ldots}$Typically, the initial force of a sudden wave is zero (f(0)=0) and thefirst order term is a rapidly rising curve, so when the impact wavereaches the sensor of the present invention, the acceleration will bedetected first. In other words, before the acceleration has actuallybegun, the present invention has already sensed the motion.

In most cases, collisions do not occur with great frequency, so if adetector detected every possible collision, it would unnecessarilycontinually alert the read/write head to leave the disk, causing seriousperformance degradation. Most collisions generate impulsiveaccelerations and acceleration rates which are described by a deltafunction whereas free-fall bodies generate a step function accelerationand delta function acceleration rate. The present invention utilizes thedifference between these two functions to differentiate whether the bodyis falling or merely has been pushed or lightly hit by another objectand thereby determine whether or not to cause the read/write head toleave the disk.

In summary, a miniature sensor according to the present invention, whendisposed on a body to be detected for free-fall motion (such as a diskdrive), utilizing piezoelectric sensing elements on a sensing structureprovides low pass filtering, elimination of external andstructure-generated high-frequency noise. The present invention, whencoupled to an interface electric circuit (such as in a notebookcomputer) senses the low frequency signal of a falling motion to providea warning for immediate damage avoidance: for example, the sensorcircuit will order the servo-mechanism of a disk drive to cause theread/write head to leave the disk). This will enhance performance, avoiddamage, and thereby increase the useful life of the device.

While the above is a full description of the specific embodiments,various modifications, alternative constructions and equivalents may beused. For example, the present invention is suitable for compact discplayers, precision instruments of all kinds, and robotic devices.Therefore, the above description and illustrations should not be takenas limiting the scope of the present invention which is defined by theappended claims.

What is claimed is:
 1. A sensor apparatus for a portable device, where said sensor apparatus has high low-frequency sensitivity and frequency selectivity to detect the gravity change as said portable device starts to free-fall, where said sensor apparatus providing a warning signal indicative of the free-fall motion of said portable device, and transmitting signals to activate a protection mechanism for said computing device.
 2. The sensor apparatus of claim 1 wherein said portable device is a computing device.
 3. The sensor apparatus of claim 2 wherein said computing device is a magnetic disk.
 4. The sensor apparatus of claim 3 wherein said magnetic disk move its read/write head away from said magnetic disk as said protection mechanism.
 5. The sensor apparatus of claim 1 wherein said frequency selectivity is implemented by a frequency selector.
 6. The sensor apparatus of claim 5 wherein said frequency selector is a piezoelectric laminate distributed on said sensor structure with a pair of electrodes disposed on it.
 7. The sensor apparatus of claim 6 wherein said frequency selector is a low frequency bandpass filter.
 8. The sensor apparatus of claim 7 wherein said low frequency bandpass filter passes a predetermined free-fall acceleration wave frequency.
 9. The sensor apparatus of claim 1 wherein said sensor apparatus has a one-dimensional sensor structure.
 10. The sensor apparatus of claim 9 wherein said one-dimensional sensor structure sense free-fall by bending motions.
 11. The sensor apparatus of claim 9 wherein said one-dimensional sensor structure sense free-fall by turning motions.
 12. The sensor apparatus of claim 9 wherein said one-dimensional sensor structure sense free-fall by compression and tension motions.
 13. A portable device having a sensor apparatus for sensing free-fall motion comprising: the said portable device a one-dimensional sensor structure functioning as said sensor apparatus having high low-frequency sensitivity to detect the gravity change as said portable device starts to free-fall; a piezoelectric laminate distributed on said one-dimensional sensor structure; a pair of electrodes disposed on said piezoelectric laminate; a frequency selector, coupled to said electrodes and piezoelectric laminate and having frequency selectivity to selecting the signal generated as a result of said free-fall signals; an electrical circuit, coupled to said frequency selector, for processing electrical signals from said frequency selector; and an activating device, coupled to said electrical circuit, for activation in response to the electrical signals. a protection mechanism, driven by said activating device, for protecting said portable device from damage.
 14. The sensor apparatus of claim 13 wherein said portable device is a computing device.
 15. The sensor apparatus of claim 14 wherein said computing device is a magnetic disk.
 16. The sensor apparatus of claim 15 wherein said magnetic disk move its read/write head away from said magnetic disk as said protection mechanism.
 17. The sensor apparatus of claim 13 wherein said sensor apparatus detects said free-fall by bending motions of said one-dimensional sensor structure.
 18. The sensor apparatus of claim 13 wherein said sensor apparatus detects said free-fall by turning motions of said one-dimensional sensor structure.
 19. The sensor apparatus of claim 13 wherein said sensor apparatus detects said free-fall by compression and tension motions of said one-dimensional sensor structure.
 20. The sensor apparatus of claim 13 wherein said at least one electrode is disposed in a predetermined shape on one surface of said piezoelectric laminate.
 21. The sensor apparatus of claim 13 wherein said at least one electrode is disposed on both surfaces of said piezoelectric laminate.
 22. The sensor apparatus of claim 13 wherein said frequency selector is a low frequency bandpass filter.
 23. The sensor apparatus of claim 22 wherein said low frequency bandpass filter passes a predetermined free-fall acceleration wave frequency.
 24. The sensor apparatus of claim 13 wherein said frequency selector utilizing the wave mode formulation and a dispersion relation of the induced motion, thereby the generating transfer functions for said sensor apparatus has an amplitude response substantially similar to a low-pass filter.
 25. The sensor apparatus of claim 24 wherein said frequency selector utilizing a modified pattern coupled to said electrodes and piezoelectric laminate to perform said low-pass filter. 